Fig. 2: Global outbreaks.
From: Endemic infectious states below the epidemic threshold and beyond herd immunity
In (a), we show a sketch with four different sub-populations, labeled i, j, k, and l, experiencing local outbreaks. Each of these outbreaks starts at a different time and has a different duration (τ). They all contribute to a global outbreak of duration τG. Such a global outbreak started with the first local outbreak in sub-population i at time t1 and finished at time t2, when the last local outbreak died out (in sub-population l). In panels (b) and (c), we show the meaning of local and global outbreaks with actual simulations. In (b), we show the total number of infected individuals (I = ∑iIi) in a particular instance of a global outbreak. This global outbreak was initiated at time t1 = 24, when the external seeding acted on the system with no other infected agent, and lasted until time t2 = 195, when the total number of infected individuals became zero. The total duration of the global outbreak is τG = t2 − t1 = 171 days. In (c), using the same realization displayed in (b), we enquire about the duration of local outbreaks. The length of horizontal lines is the duration of local outbreaks, whereas the vertical axis informs about the label of the sub-populations. One can see how local outbreaks pile up generating the global outbreak of duration τG. The parameters used to generate this example where V = 1600, β = 0.8μ, and h = 0.1 days−1 (h/V = 6.25 ⋅ 10−5).
